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# What is wrong with the suffix array approach

 0 I was solving this question https://www.hackerrank.com/contests/quantium/challenges/k-mismatch but sometimes it gives me wrong answer. What is wrong with my approach? I used suffix array and lcp array. We know that any prefix of a suffix is a substring of the string itself, so after finding the suffix array and the lcp array I did the following: I choose two suffixes say i & j, suppose suffix i smaller than j. Their lcp(i, j) will tell me the number of chars in common until I hit a mismatch or the suffix ends. if the suffix ends then we r done the number of accepted pairs is the lcp itself. otherwise if the mismatch doesn’t exceed k then we add lcp(i, j) + 1 to the result, then I start again with new suffixes. I’ll give an example to make it more clear: suffix i: abcdef suffix j: abceeeefff suppose k is 1 lcp(i, j) = 3 & the first mismatch is d & e. this mismatch doesn’t exceed k so res += (3 + 1) then new suffixes are: suffix i: ef suffix j: eeefff Notice how I removed the lcp and the mismatch. now lcp(i, j) = 1 & mismatch is f & e but the mismatch will now exceed k so we just count lcp thus res += 1 which yields res = 5 Here is a function that finds solution for i & j; LL solve(int i, int j, int n, int k) { int x = n - pos[i]; // Length of suffix i int y = n - pos[j]; // Length of suffix j // Put shorter suffix in x and longer in y if(x > y) swap(x, y), swap(i, j); LL ret = 0, m = 0; while(x > 0) { ret += lcp1[i][j]; // if all suffix i is a match break otherwise we have a mismatch if(x == lcp1[i][j]) break; // if this mismatch excceeds k then break otherwise count it if((m + 1) > k) break; m++; // remove the matched chars and mismatched char x -= (lcp1[i][j] + 1); y -= (lcp1[i][j] + 1); // update the position of the new suffixes in the suffix array. // rank returns the position of suffix starting at position pos[i] + lcp1[i][j] + 1 in //the suffix array i = rank[pos[i] + lcp1[i][j] + 1]; j = rank[pos[j] + lcp1[i][j] + 1];  } return ret + m; // return matches + mismatches } asked 16 Aug '13, 16:25 4★bondoc73 106●2●4●10 accept rate: 10%

 0 Use DP for this one. Much easier to implement. answered 16 Aug '13, 21:24 99●3●5●9 accept rate: 0% can you tell me where is the mistake in this solution? (17 Aug '13, 01:10) bondoc734★
 0 answered 17 Aug '13, 03:47 0★bpir 1 accept rate: 0%
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question asked: 16 Aug '13, 16:25

question was seen: 1,349 times

last updated: 17 Aug '13, 03:47